Computer Generated Holograms
Dr. P.W.M. Tsang
Optical Generated Holography
Hologram: Recording and reproduction of 3D scene on and from a 2D
media (such as film).
Laser
Hologram
(intercepting and recording
the magnitude and phase of
the optical wave)
Laser
Hologram
(replaying the optical
wave recorded on it)
Optical Generated Holography
What is the wavefront looks like on the hologram? Consider a single
object point.
Fresnel Zone Plate (FZP)
Only phase is shown.
Magnitude is constant.
Optical Generated Holography
What about multiple object point: superposition theory
For example, 2 object points,
FZPs added together on the
hologram
Optical Generated Holography
Mathematical expression of a FZP
𝐹𝑍𝑃 𝑥, 𝑦; 𝑧𝑚;𝑛 = 𝑒𝑥𝑝 −𝑗2𝜋𝜆−1 𝑥2 + 𝑦2 + 𝑧𝑚;𝑛2
Light from a point source spread in all directions. When intercept by an
opaque media, the optical signal will be in the form of a constant magnitude
function known as a Fresnel Zone Plate (FZP).
When more than one point sources are present, individual FZPs will sum
up on the opaque media that intercepts the optical waves. A digital
hologram can be computed on this basis.
Computer Generated Holography
Given a discrete, 3-D image, a Fresnel hologram can be generated
numerically as the real part of the product of the object and a planar
reference waves. The 3-D image can be reconstructed from the hologram
afterwards.
Computer Generated Hologram (CGH): Generation of holograms
numerically from three dimensional (3-D) models that do not actually
exist in the real world.
3D Computer graphic model
Computer Hologram filePrinter/
Displayhologram
Given a three dimensional (3D) surface with an intensity distribution I(m,n), the
Fresnel hologram is given by
Computer Generated Holography:
Fresnel Hologram
n/v
m/u
size pixel theis p
Distance of a point at (m,n) to a
point at (u,v) on the hologram
hologram thepoint toobject the
of distancelar perpendicu theis m;nz
𝑂 𝑢, 𝑣 =
𝑚=0
𝑀−1
𝑛=0
𝑁−1
𝐼 𝑚, 𝑛 𝑒𝑥𝑝 −𝑗2𝜋𝜆−1 𝑚− 𝑢 𝑝 2 + 𝑛 − 𝑣 𝑝 2 + 𝑧𝑚;𝑛2
Given a three dimensional (3D) surface with an intensity distribution I(m,n), the
Fresnel hologram is given by
Computer Generated Holography:
Fresnel Hologram
Very heavy computation.
𝑂 𝑢, 𝑣 =
𝑚=0
𝑀−1
𝑛=0
𝑁−1
𝐼 𝑚, 𝑛 𝑒𝑥𝑝 −𝑗2𝜋𝜆−1 𝑚− 𝑢 𝑝 2 + 𝑛 − 𝑣 𝑝 2 + 𝑧𝑚;𝑛2
Given a three dimensional (3D) surface with an intensity distribution I(m,n), the
Fresnel hologram is given by the convolution of I(m,n) with the FZP
Computer Generated Holography:
Fresnel Hologram
( ) ( ) ( )vuFZPvuIvuO ,,, =
( ) ( ) ( )vuFZPvuIvuO ,,, =( ) ( ) ( )vuvuvu FZPIO ,,, =
Convolution is tedious, a better way is to conduct it in the frequency space
If the hologram is complex, the object scene can be fully reconstructed
numerically
( )( )( )vu
vuvu
FZP
OI
,
,, =
With FFT, fourier transform can be performed swiftly. The hologram can be
generated with point to point multiplication, which is more computation efficient.
However, the above is only for a single plane. The computation will become more
heavy with increasing image planes.
Precompute the result of the above equation for all combinations of the 6 variables
(A,m,n,u,v,z).
Computer Generated Holography:
Fast algorithm
The memory is known as a look up table (LUT). Each cell in the LUT can be
retrieved by specifying the 6 variables as indices. Computation of the hologram is
reduced to memory look-up and simple addition.
𝐴𝑒𝑥𝑝 −𝑗2𝜋𝜆−1 𝑚 − 𝑢 𝑝 2 + 𝑛 − 𝑣 𝑝 2 + 𝑧𝑚;𝑛2
𝑂 𝑢, 𝑣 =
𝑚
𝑛
𝐿 𝐼 𝑚, 𝑛 ,𝑚, 𝑛, 𝑢, 𝑣, 𝑧𝑚;𝑛
However the memory required is extremely huge even for modern computers.
Computer Generated Holography:
Novel LUT (N-LUT)
We can infer that
𝐹𝑍𝑃 𝑚, 𝑛; 𝑧𝑚;𝑛 = 𝑒𝑥𝑝 −𝑗2𝜋𝜆−1 𝑚2 + 𝑛2 + 𝑧𝑚;𝑛2
𝑒𝑥𝑝 −𝑗2𝜋𝜆−1 𝑚− 𝑢 𝑝 2 + 𝑛 − 𝑣 𝑝 2 + 𝑧𝑚;𝑛2 = 𝐹𝑍𝑃 𝑚 − 𝑢, 𝑛 − 𝑣, 𝑧𝑚;𝑛
The LUT can be reduced to one that is dependent on 3 variables: m, n, and
𝑧𝑚;𝑛. In the LUT the values of the function 𝐹𝑍𝑃 𝑚, 𝑛; 𝑧𝑚;𝑛 (which is known
as the principal fringe pattern or the N-LUT) for all combinations of the 3
variables are stored. The hologram can be obtained as
𝑂 𝑢, 𝑣 =
𝑚
𝑛
𝐼 𝑚, 𝑛 𝐹𝑍𝑃 𝑚 − 𝑢, 𝑛 − 𝑣; 𝑧𝑚;𝑛
Computer Generated Holography:
Novel LUT (N-LUT)
The N-LUT method
Computer Generated Holography:
Novel LUT (N-LUT)
Memory size of LUT and N-LUT
• Hologram/image size = 512x512
• Intensity quantization: 256 levels.
• Number of depth planes (z) = 16
• Number of bits of each LUT entry=1 byte
LUT: 256× 512 × 512 × 512 × 512 × 16 = 281478Gbytes
N-LUT: 512 × 512 × 16 = 4.2Mbytes
The N-LUT is much smaller in size than the LUT, but a bit more
calculations (multiplying intensity with the FZP, and translating the PFP
vertically and horizontally) are required in generating the hologram.
𝑂 𝑢, 𝑣 =
𝑚
𝑛
𝐼 𝑚, 𝑛 𝐹𝑍𝑃 𝑚 − 𝑢, 𝑛 − 𝑣; 𝑧𝑚;𝑛
Computer Generated Holography:
Split LUT (S-LUT)
𝑒𝑥𝑝 −𝑗2𝜋𝜆−1 𝑚− 𝑢 𝑝 2 + 𝑛 − 𝑣 𝑝 2 + 𝑧𝑚;𝑛2
Consider the optical wave of a point source at location (m,n), falling on a pont (u,v)
on the hologram. Axial distance between point and hologram = 𝑧𝑚;𝑛.
Rewriting the equation, we have
𝑒𝑥𝑝 −𝑗2𝜋𝜆−1 Δ𝑚2 + Δ𝑛
2 + 𝑧𝑚;𝑛2 , where
Δ𝑚 = 𝑚 − 𝑢 p, Δ𝑛 = 𝑛 − 𝑣 p.
Computer Generated Holography:
Split LUT (S-LUT)
Assuming Δ𝑚 ≪ 𝑧𝑝, Δ𝑛 ≪ 𝑧𝑝, and 𝑧𝑝 is integer multiple of 𝜆, and let 𝑤𝑛 =2𝜋
𝜆, the above expression can be approximated as
𝑒𝑥𝑝 −𝑗2𝜋𝜆−1 Δ𝑚2 + Δ𝑛
2 + 𝑧𝑚;𝑛2 =e𝑥𝑝 𝑖𝑤𝑛 𝛥𝑚
2 + 𝑧𝑚;𝑛2 e𝑥𝑝 𝑖𝑤𝑛 𝛥𝑛
2 + 𝑧𝑚;𝑛2
= 𝑂𝐻 Δ𝑚, 𝑧𝑚;𝑛 𝑂𝑉 𝛥𝑛, 𝑧𝑚;𝑛 .
𝑂𝐻 Δ𝑚, 𝑧𝑚;𝑛 , 𝑂𝑉 𝛥𝑛, 𝑧𝑚;𝑛 are known as the horizontal and the vertical light modulators.
A small LUT (known as S-LUT) will be sufficient to store all combinations of the light
modulators.
Computer Generated Holography:
Split LUT (S-LUT)
Memory size of N-LUT and S-LUT
• Hologram/image size = 512x512 (Δ𝑚 or Δ𝑛 restricted to 512)• Number of depth planes (z) = 16
• Number of bits of each LUT entry=1 byte
N-LUT: 512 × 512 × 16 = 4.2Mbytes
The S-LUT is much smaller in size than the N-LUT, but a bit more
calculations (multiplying intensity with the pair of light modulators, and
computing Δ𝑚 and Δ𝑛) are required in generating the hologram.
S-LUT: 512 × 16 = 8.2Kbytes
𝑂 𝑢, 𝑣 =
𝑚
𝑛
𝐼 𝑚, 𝑛 𝑂𝐻 Δ𝑚, 𝑧𝑚;𝑛 𝑂𝑉 𝛥𝑛, 𝑧𝑚;𝑛
Computer Generated Holography:
LUT, N-LUT and S-LUT)
LUT N-LUT S-LUT
Decreasing memory size of LUT: significant
Increasing amount of computation: minor
LUT approach does not simplify the hologram formation process.
Displaying a complex hologram optically using 2 Amplitude Spatial light
modulators (SLMs)
Displaying Digital Fresnel Hologram
First Display
Real part
Second Display
Imaginary part
900 phase shifter
Reconstructed
image
Both displays are amplitude only SLM
Displaying a complex hologram optically? An Amplitude and a phase Spatial light
modulator
First Display
magnitude partReconstructed
image
Cascading an amplitude only and a phase only SLMs
Second Display
phase part
Displaying Digital Fresnel Hologram
Excerpted from J. Liu, W. Hsieh, T. Poon, and P. Tsang, "Complex Fresnel hologram display using a single SLM," Appl. Opt. 50, H128-
H135 (2011).
• Real and Imaginary holograms displayed at different vertical sections on the SLM
• The lens perform the Fourier Transform
• The sinusoidal grating couples the real and the imaginary components on the
Fourier Plane
• The signal at the output of the grating is Fourier Transform to deliver the
reconstructed image
Displaying a complex hologram optically with an amplitude-only SLM and a high resolution
grating
Displaying Digital Fresnel Hologram
Displaying a complex hologram optically with a phase-only SLM, lens and binary grating.
Any complex number can be converted into the sum of a pair of phase-only
quantities.
( ) ( ) ( ) ( ) ( )vuHvuHvuHvuivui
,,expexp, 21,, 21 +=+=
H1(u,v)
H2(u,v)
SLM Lens Binary grating Lens
f f f f
H. Song, G. Sung, S. Choi, K. Won, H. Lee, and H. Kim, "Optimal synthesis of double-phase computer generated
holograms using a phase-only spatial light modulator with grating filter," Opt. Express 20, 29844-29853 (2012).
C. Hsueh and A. Sawchuk, "Computer-generated double-phase holograms," Appl. Opt. 17, 3874-3883 (1978).
Displaying Digital Fresnel Hologram
Set the magnitude of the complex hologram to a constant value, while the
phase remains intact.
Phase only hologram
Plane WaveReconstructed
image
Disadvantage:
heavy
distortion on
the
reconstructed
image
Reconstructed image of a
complex hologram
Reconstructed image of the
phase component of a complex
hologram
Displaying a complex hologram optically in phase-only SLM without lens
Displaying Digital Fresnel Hologram
Plane WaveReconstructed
image
A 40+ years problem,
but why still an area
of immense interest?
Reconstructed image of the
phase component of a complex
hologram
Displaying a complex hologram optically in phase-only SLM without lens
Displaying Digital Fresnel Hologram
Plane Wave
Reconstructed
Image projected on
screen
Len free holographic projection system:
Electronic focusing
Enormous Market Potential
• Higher optical efficiency compares with
amplitude holograms
• Free from twin images and zero order
diffraction
• Easy to set focal plane, hence suitable for
lens free holographic projection
http://lightblueoptics.com/videos/ces-2010-light-blue-optics-personal-projector-computer/
Displaying Digital Fresnel Hologram
( ) ( )=−
−=
−
mm
m sJttts 2/exp 1
( ) ( )=
−=mm
m imsJiis expcosexp
( )sJm Bessel function.
it =−= 1Let
( ) ( )==−
−=
−
mm
m sJicisciisc exp2/exp 1
, we have
Complex modulation
Displaying Digital Fresnel Hologram
( ) ( ) ( )( )yxiyxHyxH ,exp,, =
Target hologram to be displayed
Generate a phase hologram instead
( ) ( ) ( ) ( ) yxyxyxHicyxH RP ,,cos,, −=
After mixing with the reference beam ( )Riexp
( ) ( ) ( ) ( ) ( ) yxyxyxHiicyxD RRP ,,cos,exp, −=
( ) ( ) ( )
−+−−= R
mm myxmiiyxHJc 1,exp,
Different values of m diffracts the
reconstructed beam at different angles.
When m=-1, we have
( ) ( ) ( )
−
−−= yxiiyxHJcyxDP ,exp,, 11
X. Li, J. Liu, J. Jia, Y. Pan, and Y. Wang, "3D dynamic holographic display by modulating complex amplitude experimentally," Opt.
Express 21, 20577-20587 (2013).
Complex modulation
Displaying Digital Fresnel Hologram
( ) ( ) ( )( )yxiyxHyxH ,exp,, =
Target hologram to be displayed
Generate a phase hologram instead
( ) ( ) ( ) ( ) yxyxyxHicyxH RP ,,cos,, −=
After mixing with the reference beam ( )Riexp
( ) ( ) ( ) ( ) ( ) yxyxyxHiicyxD RRP ,,cos,exp, −=
( ) ( ) ( )
−+−−= R
mm myxmiiyxHJc 1,exp,
Different values of m diffracts the
reconstructed beam at different angles.
When m=-1, we have
( ) ( ) ( )
−
−−= yxiiyxHJcyxDP ,exp,, 11
Phase hologram
m=0
m=-1
m=-2
m=1
m=2
Complex modulation
Displaying Digital Fresnel Hologram
Phase hologram
m=0
m=-1
m=-2
m=1
m=2
( ) ( ) yxiyxH ,exp,
Optical filter
Lens Filter LensSLM
f f f f
Displaying a complex hologram optically in phase-only SLM without lens: Macropixel
Double Phase Macro Pixel Hologram
( ) ( ) ( ) vuivuivuH
,, 21 expexp5.0,
+=
21 22
If resolution of SLM is high enough, spatial multiplex the pair of phase components in a
uniform manner
V. Arrizón and D. Sánchez-de-la-Llave, "Double-phase holograms implemented with phase-only spatial light
modulators: performance evaluation and improvement," Appl. Opt. 41, 3436-3447 (2002).
Double Phase Macro Pixel Hologram
( ) ( ) ( ) vuivuivuH
,, 21 expexp5.0,
+=
V. Arrizón and D. Sánchez-de-la-Llave, "Double-phase holograms implemented with phase-only spatial light
modulators: performance evaluation and improvement," Appl. Opt. 41, 3436-3447 (2002).
It can be proved that the magnitude and phase components of the hologram can be derived
from the pair of phase angles 𝜃1 and 𝜃2.
Spatial division multiplexing of the pair of phase components is a downsampling process that
can lead to aliasing error.
Different spatial division multiplexing of the pair of phase components can lead to different
quality of the reconstructed images. Lets have a look at 2 popular multiplexing topologies, the
1 × 2 and the 2 × 2 macro pixel format.
Evaluation on reconstructed images (intensity amplified by around 10 times).
Double Phase Macro Pixel Hologram
21 22
The method is fast and the visual quality is good.
Noise is prominent in the 1x2 structure, and less in the 2x2 structure.
The intensity is low.
P.W.M. Tsang, "Generation of phase-only hologram", Proc. SPIE 9271, Holography, Diff. Opts, and Apps VI, 92711Q, 2014.
Converting complex hologram to phase only image using the iterative
approach
Phase only hologram
Plane Wave Reconstructed
image
Adjust the phase only hologram until the reconstructed image is same as
the target ones.
Disadvantage:
heavy amount of
computation in the
iterative process,
especially if multiple
depth images is
involved.
Comparator
target
image
Displaying Digital Fresnel Hologram
Generating phase-only Fourier hologram from an image using the
iterative approach, based on principles of GSA.
1. Given an image I(x,y), to
be converted to a
hologram.
2. Generated the Fourier
hologram H(x,y) for I(x,y).
3. Keep the phase
component, and revert
back to the spatial image
with IFT,
4. Get the image and the
phase of the inverse
transformed hologram.
5. Repeat 2 to 4 until the
error is smaller than a
threshold.
Gerchberg Saxton algorithm (GSA)
iterative Fourier transform algorithm (IFTA).
Generating phase-only Fresnel hologram from an image using the
iterative Fresnel transform algorithm (IFTA).
1. Given an image I(x,y), to be
converted to a hologram.
2. Generated the Fresnel
hologram H(x,y) for I(x,y).
3. Keep the phase component,
and revert back to the spatial
image with inverse Fresnel
transform,
4. Get the image and the phase of
the inverse Fresnel transfomred
hologram.
5. Repeat 2 to 4 until the error is
smaller than a threshold.
Gerchberg Saxton algorithm (GSA)
Generating phase-only Fresnel hologram from an image using the
iterative Fresnel transform algorithm (IFTA).
Gerchberg Saxton algorithm (GSA)
(a) Source image “Peppers”, (b) Phase-only hologram of the image “Peppers”, obtained with the GSA, (c)
Rconstructed image of the phase-only hologram in (b).
Mixed-region Amplitude Freedom (MRAF)
1. Source image is divided into a signal and a noise region.
2. For the signal region, amplitude constraint is imposed.
3. For the noise region, there is no amplitude constraint.
𝐼𝑃𝑡𝐸 𝑚,𝑛 = ൝
𝐼𝐸 𝑚,𝑛 𝑖𝑓 𝑚, 𝑛 ∈ 𝑆
𝐽𝑡𝐸 𝑚, 𝑛 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Noise region provides
additional freedom to
absorb the error in the
signal region
Mixed-region Amplitude Freedom (MRAF)
(a) Source image “Apple” (b) Reconstructed image of phase-
only hologram obtained with 5
rounds of MRAF
(c) Signal region of reconstructed
image
(d) Reconstructed image of phase-
only hologram obtained with 5
rounds of IFTA
Random noise addition (RNA)
𝐼𝑁 𝑚, 𝑛 = 𝐼 𝑚, 𝑛 × ℵ 𝑚, 𝑛 = 𝐼 𝑚, 𝑛 × 𝑒𝑥𝑝 𝑖𝜃 𝑚, 𝑛 .
Simulate the effect of overlaying an optical diffuser onto the image.
The diffuser scatters the optical waves so that its magnitude distribution is roughly
homogeneous on the hologram. The phase component alone, therefore, is sufficient
to represent the hologram.
𝜃 𝑚, 𝑛 is a 2-D array of random values in the range ሾ0,2𝜋).
To generate a phase-only hologram, the image is first added without random phase
noise, and converted into a Fresnel hologram. The magnitude of the hologram is set
to unity, resulting in a phase-only hologram.
However, the reconstructed image is contaminated with noise.
Random noise addition (RNA)
(a) Intensity distribution of
a double-depth image.
(b) Depth map of the double-
depth image.
(c) Phase-only hologram
obtained with RNA.(d) Reconstructed image on
first depth plane.(e) Reconstructed image on
second depth plane.
One Step Phase Retrieval Phase Only Hologram
E. Buckley, “Holographic laser projection technology,” Proc. SID Symp., 1074–1078 (2008)
Reconstructed images of hologram
sub-frames are displayed
sequentially at high frame rate. The
noise is smoothed out with
persistence of vision of human
eyes
Multiple Sub-frames One Step Phase Retrieval
(a) (b) and (c): Simulated reconstructed image of a single phase-only hologram of the source image “Lenna”,
generated by the OSPR method, based on 1, 5, and 15 phase-only hologram(s), respectively.
Multiple frames are required, and noise may not average out completely.
Restricted to object scene with specific characteristics (e.g. diffusive).
Advantages: Faster than iterative methods, and favorable visual quality on
the reconstructed images.
Very high frame rate is required, increasing the requirement and cost of the
display device.
Intensive computation required to generate multiple frame holograms for a
given object scene, especially for large hologram size.
Disadvantages
One Step Phase Retrieval Phase Only Hologram
• Scan each row of the complex hologram from left to right.
• Forced the magnitude of each scanned pixel to unity
• Diffuse error to the neighborhood, unvisited pixels (Floyd-Steinberg error diffusion)
Advantage: Low complexity and high reconstructed
image quality
p0 p1
p3p2 p4
Complex hologram
Phase only hologram
Force
magnitude to a
constant value
Last
pixel?
Diffuse error to
neighboring
pixelsNo
Yes P. Tsang and T. Poon, "Novel method for converting digital Fresnel hologram to phase-only
hologram based on bidirectional error diffusion," Opt. Express 21, 23680-23686 (2013).
Uni-directional Error Diffusion (UERD)
Phase Only Hologram
( ) ( ) ( )jjjjjj yxEwyxHyxH ,1,1, 1+++
( ) ( ) ( )jjjjjj yxEwyxHyxH ,1,11,1 2+−+−+
( ) ( ) ( )jjjjjj yxEwyxHyxH ,,1,1 3+++
( ) ( ) ( )jjjjjj yxEwyxHyxH ,1,11,1 4+++++
16/71 =w
16/32 =w
16/53 =w16/14 =w
Error
Uni-directional Error Diffusion (UERD)
Phase Only Hologram
Original images
Reconstructed images from the phase components of the holograms
Uni-directional Error Diffusion (UERD)
Phase Only Hologram
Computer Generated Holography:
Fresnel Hologram
Original images
Reconstructed images from UERD holograms (noise is noted)
Uni-directional Error Diffusion (BERD)
Phase Only Hologram
Bi-directional Error Diffusion (BERD)
Phase Only Hologram
• Scan odd row of the complex hologram from left to right
• Scan even row of the complex hologram from right to left.
• Forced the magnitude of each scanned pixel to unity
• Diffuse error to the neighborhood, unvisited pixels
Odd rows Even rows
Partially de-correlates the error from the signal
P. Tsang and T. Poon, "Novel method for converting digital Fresnel hologram to phase-only hologram based on bidirectional
error diffusion," Opt. Express 21, 23680-23686 (2013).
Bi-directional Error Diffusion (BERD) Phase Only
Hologram
Original images
Reconstructed images from BERD holograms (noise is reduced)
Localized error diffusion with redistribution
(LERDR) phase only hologram
•Partition a hologram uniformly into vertical segments
•Apply localized error diffusion to each segment to convert the pixels into phase only value
•Apply low pass filtering to redistribute the error
A segment with M pixels
If not the last pixel,
force the magnitude to
unity, and distribute the
error to the 4
neighboring pixels
For the last pixel, force
the magnitude to unity,
and distribute the error
to the 3 neighboring
pixels below it
P. Tsang, A. Jiao, and T. Poon, "Fast conversion of digital Fresnel hologram to phase-only hologram based on localized error diffusion and
redistribution," Opt. Express 22, 5060-5066 (2014).
Sampled Phase Only Hologram
Phase only hologram
Down-sampled
with a grid-cross
lattice
Convert to a
complex
hologram
Source image
Retain phase
component only
𝑆0 𝑥, 𝑦 = ቊ1 𝑖𝑓 𝑥%𝜏 = 00 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
,
𝑆1 𝑥, 𝑦 = ቊ1 𝑖𝑓 𝑦%𝜏 = 00 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
,
𝑆2 𝑥, 𝑦 = ቊ1 𝑖𝑓 𝑥%𝜏 = 𝑦%𝜏0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
,
𝑆3 𝑥, 𝑦 = ቊ1 𝑖𝑓 𝑥%𝜏 = 𝜏 − 𝑦%𝜏0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
.
𝑆 𝑥, 𝑦 = ራ
𝑘=0
3
𝑆𝑘 𝑥, 𝑦
𝜏
𝜏
Sampled Phase Only Hologram
Evaluation on reconstructed
images
Fast, only involves a down-sampling process.
The reconstructed image is bright with favorable visual quality.
On the down-side, a texture is overlaid onto the reconstructed image.
Case study on a new method for
holographic projection
Optical reconstruction setup
LASERSLM
BEAM
EXPANDER MIRROR
MIRROR
Sampled Phase Only Hologram
Optical reconstructed images of a hologram representing single depth image.
The down-sampling texture is not prominent.
Optical reconstructed images of a hologram representing a double depth image.
Case study on a new method for
holographic projection
Easy to assign different focal length to different part of the projected image
Projection can be
adaptive to
screen geometryPlane Wave
Phase only
holographic
display